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- Tuomas Airaksinen, Erkki Heikkola, Anssi Pennanen, Jari Toivanen
- J. Comput. Physics
- 2007

A preconditioner defined by an algebraic multigrid cycle for a damped Helm-holtz operator is proposed for the Helmholtz equation. This approach is well-suited for acoustic scattering problems in complicated computational domains and with varying material properties. The spectral properties of the precondi-tioned systems and the convergence of the GMRES… (More)

Efficient numerical methods for pricing American options using Heston's stochastic volatility model is proposed. Based on this model the price of a Eu-ropean option can be obtained by solving a two-dimensional parabolic partial differential equation. For an American option the early exercise possibility leads to a lower bound for the price of the option.… (More)

- Ferrante Neri, Jari Toivanen, Raino A. E. Mäkinen
- Appl. Intell.
- 2007

- Jari Toivanen
- 1998

A multiobjective multidisciplinary design optimization (MDO) of two-dimensional airfoil is presented. In this paper, an approximation for the Pareto set of optimal solutions is obtained by using a genetic algorithm (GA). The rst objective function is the drag coeecient. As a constraint, it is required that the lift coeecient is above a given value. The CFD… (More)

- Samuli Ikonen, Jari Toivanen
- Appl. Math. Lett.
- 2004

- Kazufumi Ito, Jari Toivanen
- SIAM J. Scientific Computing
- 2009

The deterministic numerical valuation of American options under Heston's stochastic volatility model is considered. The prices are given by a linear com-plementarity problem with a two-dimensional parabolic partial differential operator. A new truncation of the domain is described for small asset values while for large asset values and variance a standard… (More)

Stochastic volatility models lead to more realistic option prices than the Black-Scholes model which uses a constant volatility. Based on such models a two-dimensional parabolic partial differential equation can derived for option prices. Due to the early exercise possibility of American option contracts the arising pricing problems are free boundary… (More)

- Kaisa Miettinen, Marko M. Mäkelä, Jari Toivanen
- J. Global Optimization
- 2003

- Kazufumi Ito, Jari Toivanen
- Appl. Math. Lett.
- 2006

- S. Ikonen, J. Toivanen
- 2004

Option pricing models with a stochastic volatility are more realistic than the Black-Scholes model which uses a constant volatility. The prices of options based on such models can be obtained by solving a parabolic partial differential equation. Particularly, we consider the model presented by Heston. The variables in these problems are the time, the… (More)